# On the Hypomonotone Class of Variational Inequalities

arXiv: https://arxiv.org/abs/2410.09182 · HTML: https://mlsanity.com/paper/2410.09182/

## Key facts

- Cited by 1 papers in the map (data through 14 Oct 2026).
- Builds on 5 of its 13 references that are in the map.
- First posted on arXiv 11 Oct 2024.

## Builds on (most cited first, 5 of 5)

- [Towards Deep Learning Models Resistant to Adversarial Attacks](https://mlsanity.com/paper/1706.06083/) (2017)
- [Intriguing properties of neural networks](https://mlsanity.com/paper/1312.6199/) (2013)
- [Multi-Agent Actor-Critic for Mixed Cooperative-Competitive Environments](https://mlsanity.com/paper/1706.02275/) (2017)
- [A causal framework for distribution generalization](https://mlsanity.com/paper/2006.07433/) (2020)
- [Minimax Classification with 0-1 Loss and Performance Guarantees](https://mlsanity.com/paper/2010.07964/) (2020)

## Built on by (most cited first, 1 of 1)

- [On the Computational Complexity of Performative Prediction](https://mlsanity.com/paper/2601.20180/) (2026)

## Abstract (arXiv)

This paper studies the behavior of the extragradient algorithm [Korpelevich, 1976] when applied to hypomonotone operators, a class of problems that extends beyond the classical monotone setting. To support the understanding of this variational inequality problem class, we focus on a subclass of hypomonotone linear operators, characterizing them based on their eigenvalues and providing concrete examples. While the extragradient method is widely recognized for its efficiency in solving variational inequalities involving monotone and Lipschitz continuous operators, we demonstrate that it does not guarantee convergence in the hypomonotone case. In particular, we construct a counterexample where the extragradient method diverges regardless of the step size. A numerical experiment is presented to support this result.